In order to measure properties of ultrathin films, e.g. film thickness, densities and roughness, using X-rays, X-rays may be passed through the sample at grazing incidence angles nearly parallel to the surface of the film. Multiple measurements are taken at different angles. Calculations are then carried out to determine properties of the sample from the measured results. Such a measurement is referred to as grazing incident X-ray reflectivity, abbreviated as GIXRR or GIXR or XRR. In this application, GIXR will be used.
The direct determination of thin film properties from GIXR data is not possible therefore the parameters of studied films have to be determined by fitting of a simulated (calculated) GIXR curve to a measured curve. The parameters of the simulated GIXR curve are adjusted such that mismatch between measured and simulated data is minimal. One approach, for calculations is to use the model which has a plurality of layers, each with a film thickness, density, and interface roughness {Windt, 1998 #109}.
This approach can work well in certain circumstances, in particular if the thin film has thin interfaces and the layers have constant density. However, in the majority of cases thin films grown by physical sputtering techniques can form chemical compounds at the interfaces, and further the thickness of the interface can be comparable to the thickness of the film.
Another example where this method can fail is in the case of relatively thick films which do not have a constant density profile.
To analyse films with low absorption a “groove tracking method” can be used. This assumes that the sample has a set of thin sublayers, each of which has a thickness much less than the actual thickness of each of the sub-layers. Each of the j sublayers has a corresponding refractive index nj. The calculation varies the real part of refractive index of each of the sublayers until the best possible match to the observed results is obtained.
See in particular the paper “Model-independent method for reconstruction of scattering-length-density profiles using neutron or x-ray reflectivity data”, Xiao-Lin Zhou and Sow-Hsin Chen, Physical Review E, Volume 47, Number 5, pages 3174 to 3190, June 1993 for a description of the method.
However, this approach also has problems. Calculations by the groove method are not wholly reliable and in particular the method can produce many unphysical solutions, i.e. the calculations can converge on a result that does not match physical reality.
There is accordingly a need for an improved method of measuring properties of ultrathin films.